To offset some of the developement costs of competing teams, NASA could offer some of their reseach and testing facilities to competitors free of charge.

In this way smaller prizes would become more attractive and prospective competitors would not be scared of the development costs involved. Competitors would have to attain milestones before facilities were made available to them and NASA would not be allowed to make any data available to other teams, although they could possibly use it themselves (with built in time delays to allow the competitor to fully have the chance to develope a concept first).

I'm sure that individual NASA engineers would not only test but help teams overcome problems on an unofficial basis turing trials, official NASA input should be avoided at all costs.

Like most big organisations NASA probably has extra capacity and this could be utilised to help teams at very little cost to NASA, afterall they would have to pay to maintain the facilities anyway.

The work on the CEV is to a high degree done by private companies including Scaled Composites.

So NASA has to buy the CEV in principle. But they cannot buy and use private constructed and built spacecrafts without testing them and testing their components. On the other side the private firms won't build spacecrafts for NASA if there is a too large risk that NASA will refuse the whole vehicle.

As a consequence NASA will open their facilities for cooperation with the privates at least.

If they will buy a vehicle in future they didn't order and was constructed for private space travel this too will cause their facilities to be open for the private producer I suppose.